SW(3/2, 2) superconformal algebra is W algebra with two Virasoro operators. The Kac determinant is calculated and the complete list of unitary representations is determined. Two types of extensions of SW(3/2, 2) algebra are discussed. A new approach to construction of W algebras from rational conformal field theories is proposed.
The SW(3/2, 3/2, 2) superconformal algebra is a W algebra with two free parameters. It consists of 3 superconformal currents of spins 3/2, 3/2 and 2. The algebra is proved to be the symmetry algebra of the coset su(2)⊕su(2)⊕su(2) su(2). At the central charge c = 10 1 2 the algebra coincides with the superconformal algebra associated to manifolds of G 2… (More)
BACKGROUND Determining the function of regulatory elements is fundamental for our understanding of development, disease and evolution. However, the sequence features that mediate these functions are often unclear and the prediction of tissue-specific expression patterns from sequence alone is non-trivial. Previous functional studies have demonstrated a link… (More)
Parafermionic conformal field theories are considered on a purely algebraic basis. The generalized Jacobi type identity is presented. Systems of free fermions coupled to each other by nontrivial parafermionic type relations are studied in detail. A new parafermionic conformal algebra is introduced, it describes the sl(2|1) 2 /u(1) 2 coset system.
Association studies have identified a number of loci that contribute to an increased body mass index (BMI), the strongest of which is in the first intron of the FTO gene on human chromosome 16q12.2. However, this region is both non-coding and under strong linkage disequilibrium, making it recalcitrant to functional interpretation. Furthermore, the FTO gene… (More)
We present a new conformal algebra. It is Z 2 × Z 2 graded and generated by three N = 1 superconformal algebras coupled to each other by nontrivial relations of parafermionic type. The representation theory and unitary models of the algebra are briefly discussed. We also conjecture the existence of infinite series of parafermionic algebras containing many N… (More)
Quantum hamiltonian reduction of affine superalgebras is studied in the twisted case. The Ramond sector of " minimal " superconformal W-algebras is described in detail, the determinant formula is obtained. The paper generalizes the results of Kac and Wakimoto to the twisted case.